A Coarse Jacquet-Zagier Trace Formula for GL(n) with Applications

Author: Yang, Liyang

Year: 2021

Degree: Dissertation (Ph.D.)

Advisor: Ramakrishnan, Dinakar

Committee Members: Zhu, Xinwen; Ramakrishnan, Dinakar; Mantovan, Elena; Burungale, Ashay

Option: Mathematics

DOI: 10.7907/1j4r-pv26

Abstract

In this thesis we establish a coarse Jacquet-Zagier trace identity fo GL(n). This formula connects adjoint L-functions on GL(n) with Artin L-functions attached to certain induced Galois representations. We prove the absolute convergence when Re(s) > 1, and obtain holomorphic continuation under almost all character twists. Moreover, as an application, we obtain that holomorphy of certain adjoint L-functions for GL(n) implies Dedekind conjecture of degree n. Some nonvanishing results are also proved.

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